mlsanityData to 14 Oct 2026

Bayesian Physics Informed Neural Networks for Reliable Transformer Prognostics

arXiv 2509.15933 ↗First posted 19 Sep 2025cs.LG cs.SY eess.SYcited by 3

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Abstract (arXiv)

Scientific Machine Learning (SciML) integrates physics and data into the learning process, offering improved generalization compared with purely data-driven models. Despite its potential, applications of SciML in prognostics remain limited, partly due to the complexity of incorporating partial differential equations (PDEs) for ageing physics and the scarcity of robust uncertainty quantification methods. This work introduces a Bayesian Physics-Informed Neural Network (B-PINN) framework for probabilistic prognostics estimation. By embedding Bayesian Neural Networks into the PINN architecture, the proposed approach produces principled, uncertainty-aware predictions. The method is applied to a transformer ageing case study, where insulation degradation is primarily driven by thermal stress. The heat diffusion PDE is used as the physical residual, and different prior distributions are investigated to examine their impact on predictive posterior distributions and their ability to encode a priori physical knowledge. The framework is validated against a finite element model developed and tested with real measurements from a solar power plant. Results, benchmarked against a dropout-PINN baseline, show that the proposed B-PINN delivers more reliable prognostic predictions by accurately quantifying predictive uncertainty. This capability is crucial for supporting robust and informed maintenance decision-making in critical power assets.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 23 of its 50 references that are in the map. First posted on arXiv 19 Sep 2025.

Builds on

23 of 50 references.

References · 23

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  3. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
  4. 2024KAN: Kolmogorov-Arnold Networkscited by 649
  5. 2021Physics-Informed Neural Operator for Learning Partial Differential Equationscited by 527
  6. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 170
  7. 2018Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problemscited by 147
  8. 2021Deep physical neural networks enabled by a backpropagation algorithm for arbitrary physical systemscited by 128
  9. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  10. 2023Residual-based attention in physics-informed neural networkscited by 72
  11. 2022Bayesian Physics-Informed Neural Networks for real-world nonlinear dynamical systemscited by 54
  12. 2020Fusing Physics-based and Deep Learning Models for Prognosticscited by 40
11 more
  1. 2023Uncertainty Quantification in Machine Learning for Engineering Design and Health Prognostics: A Tutorialcited by 27
  2. 2021BNNpriors: A library for Bayesian neural network inference with different prior distributionscited by 20
  3. 2025Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemblecited by 13
  4. 2024Residual-based Attention Physics-informed Neural Networks for Spatio-Temporal Ageing Assessment of Transformers Operated in Renewable Power Plantscited by 11
  5. 2023A Benchmark on Uncertainty Quantification for Deep Learning Prognosticscited by 9
  6. 2024Conformalized Physics-Informed Neural Networkscited by 7
  7. 2022Conformal Prediction Intervals for Remaining Useful Lifetime Estimationcited by 3
  8. 2025Improved Uncertainty Quantification in Physics-Informed Neural Networks Using Error Bounds and Solution Bundlescited by 3
  9. 2024A Hybrid Probabilistic Battery Health Management Approach for Robust Inspection Drone Operationscited by 2
  10. 2025Scalable Bayesian Physics-Informed Kolmogorov-Arnold Networkscited by 2
  11. 2024Towards a Probabilistic Fusion Approach for Robust Battery Prognosticscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 1; 2026: 2.

3 papers.

  1. 2026PAD-Hand: Physics-Aware Diffusion for Hand Motion Recoverycited by 4
  2. 2025Physics-Informed Machine Learning for Transformer Condition Monitoring -- Part II: Physics-Informed Neural Networks and Uncertainty Quantificationcited by 0
  3. 2026Disentangling Aleatoric and Epistemic Uncertainty in Physics-Informed Neural Networks. Application to Insulation Material Degradation Prognosticscited by 0